×

# Inequalities: Part 1

Prove that:

$$\displaystyle ab(a+b)+bc(b+c)+ac(a+c)\geq \sum_{cyclic}ab\sqrt{\frac{a}{b}}(b+c)(c+a)$$

where, $$\displaystyle \sum_{cyclic}ab\sqrt{\frac{a}{b}}(b+c)(c+a)=ab\sqrt{\frac{a}{b}}(b+c)(c+a)+bc\sqrt{\frac{b}{c}}(c+a)(a+b)+ca\sqrt{\frac{c}{a}}(a+b)(b+c)$$

So, prove that:

$$\displaystyle ab(a+b)+bc(b+c)+ac(a+c)\geq ab\sqrt{\frac{a}{b}}(b+c)(c+a)+bc\sqrt{\frac{b}{c}}(c+a)(a+b)+ca\sqrt{\frac{c}{a}}(a+b)(b+c)$$

Note by Saurabh Mallik
1 year, 6 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

## Comments

There are no comments in this discussion.

×

Problem Loading...

Note Loading...

Set Loading...